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As the demand for multimedia traffic via satellite increase, quality of service (QoS) management becomes more crucial, especially for the effective utilization of on-board switching capabilities of multi-beam satellite system. For multimedia services, parameters related to different requirements need to be evaluated in terms of delay, jitter, blocking probability and burstiness. This paper is on the evaluation of QoS parameters associated with the transmission of multimedia information including voice, video and data through satellite on-board ATM switching network by using various onboard switching algorithms and queueing analyses. Specifically, we evaluate and compare the performance of on-board switching algorithm of Djikstra, Bellman-Ford, and K-shortest path on the most efficient ATM network (Banyan, Benes, and Batcher-Banyan networks) along with M/G/1 queuing system. The parameters used for MF-TDMA uplink and TDM downlink simulations include: end-to-end delay, queuing delay, burstiness factor for varying traffic load on the network, and blocking probability for various holding time. Results show that, for small and medium size networks, Djikstra's algorithm is most effective in terms of delay whereas K-shortest path algorithm is most effective for large network. Towards low blocking probability and burstiness factor, the Batcher-Banyan ATM network with the single server M/G/1 queue is most efficient.